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Atomic orbitals: 3p

The shape of the three 3p orbitals. From left to right: 3pz, 3px, and 3py. For each, the gold zones are where the wave functions have negative values and the copper zones denote positive values.

For any atom, there are three 3p orbitals. These orbitals have the same shape but are aligned differently in space. The three 3p orbitals normally used are labelled 3px, 3py, and 3pz since the functions are "aligned" along the x, y, and z axes respectively.

Each 3p orbital has four lobes. There is a planar node normal to the axis of the orbital (so the 3px orbital has a yz nodal plane, for instance). Apart from the planar node there is also a spherical node that partitions off the small inner lobes. The higher p-orbitals (4p, 5p, 6p, and 7p) are more complex still since they have more spherical nodes.

The origin of the planar node becomes clear if we examine the wave equation which, for instance, includes an x term in the case of the 3px orbital. Clearly When x = 0, then we must have a node, and this by definition is the yz plane.

The origin of the spherical node becomes clear if we examine the wave equations, which includes (4 - ρ) terms. When (4 - ρ) = 0, then we must have nodes. Since for any 3p orbital ρ = 2Zr/3 (Z = effective nuclear charge, r = radius in atomic units), then the nodes are at the radius for which (4 - 2Zr/3) = 0, that is, r = 6/Z atomic units.

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Document served: Wednesday 21st October, 2020